If a kernel \(\kappa \)  is positive definite, the potential of any \(\mu \in \mathcal {E}\)  is (well defined and) finite quasi-everywhere on \(X\)  [1]}; furthermore, the potentials of any two given \(\mu ,\nu \in \mathcal {E}\)  are equal nearly everywhere on \(X\)  if and only if \(\Vert \mu -\nu \Vert =0\)  [1]}. Therefore, for a strictly positive definite kernel \(\kappa \) ,
\(\kappa \mu =\kappa \nu \text{ \ n.e.\ on $X$}\iff \mu =\nu .\) 
